Scolari had set the semi-finals as his target before the tournament and said that, now it had been reached, he wanted to go all the way.
Portugal, who won 6-5 on penalties after the match had finished 2-2 after extra time, have never won a major tournament but are in the championship's semi-finals for the second time in a row. They lost to France at Euro 2000.
"We have done what we set out to do, now we are dreaming of a lot more," said the Brazilian, who led his own country to World Cup victory two years ago. On that occasion, they also knocked out Sven-Goran Eriksson's England in the quarter-finals.
"We have evolved...now we have to dream and the dream is to reach the final."
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In particular, he wanted to thank a group of fisherman who saluted the team from the river.
"Those fisherman are always waiting for us in their boats," he said. "I dedicate this victory to them."
He added: "I feel the same happiness as all the Portuguese. Although I'm Brazilian, I'm just as enthusiastic as they are."
Scolari said Swiss referee Urs Meier was right to disallow a Sol Campbell goal in the 90th minute which would have given England a 2-1 win in normal time.
"I think it was a foul and the referee gave it. I have nothing to say about it," he said.
Scolari was also asked whether his substitutions were down to luck or inspired coaching after Helder Postiga and Rui Costa both scored after coming on.
"As a lot of people say I don't work, it's luck, a lot of luck," he said. "I have won 16 lucky titles in my career."
